Quanta of fields

Quanta of fields is in the vocabulary of Quantum Field Theory( QFT). QFT is a mathematical theory where a differential operator operates on a field, creating a "quantum" of that field.The "quantum" and the "field" are two different mathematical functions.

For example take the QFT of elementary particle physics. The Standard Model (SM) has a table with axiomatically defined elementary particles, which have the masses and quantum numbers in the table, and are point particles . This QFT axiomatically assumes that each particle in the table is a field extending all over space time. Mathematically this field is represented by the plane wave solution of the given particle, solution to its appropriate equation ( Dirac for electrons...) On these fields differential creation and annihilation operators operate, creating or annihilating a particle. The formalism leads to Feynman diagrams that allow the calculation of the interaction of particles, because the diagram represents pictorially a term in the solution of the scattering equation.

Thus fields and particles have a different mathematical representation.